Research Highlights

Math Dream
New Connections of Representation Theory to Algebraic Geometry and Physics Representation theory is formally a branch of algebra which studies algebraic structure of symmetries. Its role in contemporary mathematics is due to the fact – realized through major discoveries of the 19th and 20th centuries mathematics – that the structure of symmetries […]

Travel Time Tomography
Inverse Problems are problems where causes for a desired or observed effect are to be determined. They arise in all fields of science and technology. An important example is to determine the density distribution inside a body from measuring the attenuation of Xrays sent through this body, the problem of “Xray tomography.” […]

A New (Math) World
A new mathematical object was revealed during a lecture at the American Institute of Mathematics (AIM). Two researchers from the University of Bristol exhibited the first example of a third degree transcendental Lfunction. These Lfunctions encode deep underlying connections between many different areas of mathematics. The news caused excitement at the AIM […]

When The Volcano Blows
“I don’t know where I’m gonna go when the volcano blows”. So wrote Jimmy Buffet. The more important challenge for volcanologists, however, is to determine “When should we go before the volcano blows!” Tackling this challenge was a principal focus of a group¹ of statisticians, mathematicians and volcanologists at SAMSI last year. […]

Better Seismic Imaging
The economic value to the oil industry of 3D seismic imaging is approximately $11 billion annually. How accurately seismic imaging can be done depends on both the quality of the sensing equipment, but also very much on the effectiveness of the mathematical algorithms that are used. Hence it is an important event when seismic imaging […]

Sparse Representations
What do researchers studying infrared spectroscopy, seismic imaging, error correcting codes, and MRI’s have in common? They all can get better results if they have the right math. Fourier analysis, discovered in analyzing the flow of heat, revolutionized how mathematics is used in a variety of sciences by breaking complicated functions into a sum of […]

EvoGeo
Can polyhedral geometry and commutative algebra—usually regarded as pure mathematics—help biologists? We at the IMA certainly think so, and the emerging applications of these mathematical areas to evolutionary biology was a major theme during a workshop bringing 135 mathematicians, statisticians, biologists, and computer scientists to the IMA in March 2007 as part of our yearlong […]

Honeybee Olfaction
A honeybee may forage on 1,000s of flowers for nectar and pollen in its lifetime. Scent is one of the primary means that it uses for identifying rewarding flowers. How honeybees and other animals learn to associate complex and variable scents with important events is still not well understood. Honeybees are an excellent model system […]

New Tools for Old Problems
When mathematicians notice connections between two distinct areas of their discipline, you can be sure something interesting will develop. That is exactly what happened at a recent workshop at the American Institute of Mathematics (AIM). The scientific advisory board of AIM noticed that new methods in ergodic theory, a subject arising from […]

Neuronal Network
Modeling the Dynamic Range of a Neuronal Network for Breathing For humans and other mammals, breathing is essential to life. The breathing rhythm relies on an area of the brain stem known as the preBötzinger complex, a network of neurons exhibiting rhythmic bursts of activity that […]